Topology Unit
In mathematics, topology is the study of the properties of space that are preserved under the continuous deformations, such as stretching, twisting, crumpling, and bending, but not tearing or gluing.  For this reason, topology is often referred to as “the rubber sheet geometry”.  

Topology developed as a field of study out of geometry and set theory, through the analysis of concepts such as space, dimension, and transformation.  Leonhard Euler’s Seven Bridges of Königsberg Problem and the Euler Characteristic are arguably the field’s first theorems.  
Picture
Johann Benedict Listing (1808 - 1882)
Johann Benedict Listing introduced the term topology in the 19th century, although it was not until the first decades of the 20th century that the idea of a topological space was developed.  By the middle of the 20th century, topology had become a major branch of mathematics.
One of the most famous shapes in topology is a Möbius strip, named after the German mathematician August Ferdinand Möbius.   In one of those strange quirks of mathematical fate, Möbius was not actually the first to discover or describe the object.  Credit should go to Johann Benedict Listing.  Working independently, Listing first encountered the surface in July 1858.  He published his discovery in an 1861 paper devoted to generalizations of Euler’s formulas for polyhedra.
Picture
August Ferdinard Möbius (1790 - 1868)
Lecture Notes & Other Resources